Fractions in Number Stories

Transcription

1 Fractions in Number Stories Objective To provide experiences with solving number stories involving fractions. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Use pennies, counters, or pictures to solve fraction number stories. [Number and Numeration Goal ] Describe solution strategies for solving fraction number stories. [Number and Numeration Goal ] Use Fraction Cards to compare fractions. [Number and Numeration Goal ] Measure and draw a line segment to the nearest _ inch. [Measurement and Reference Frames Goal ] Key Activities The teacher and children make up and solve number stories involving fractions. Children practice solving fraction number stories independently. Ongoing Assessment: Informing Instruction See page 89. Ongoing Assessment: Recognizing Student Achievement Use journal page 0. [Number and Numeration Goal ] Materials Math Journal, pp. 00 and 0 Home Link 8 7 inch ruler pennies or counters (optional) Fraction Cards (optional) tool-kit clock (optional) slate Reviewing the Line Plot Routine Student Reference Book, pp stick-on notes Children describe landmarks on a line plot and compare chances for two different events. Math Boxes 8 8 Math Journal, p. 0 Children practice and maintain skills through Math Box problems. Home Link 8 8 Math Masters, p. Children practice and maintain skills through Home Link activities. ENRICHMENT Solving Math Curse Number Stories Math Curse paper Children solve and write fraction number stories based on those found in the book Math Curse. EXTRA PRACTICE Minute Math + Minute Math +, pp. 8, 90, 9, and Children solve number stories with fractions. Advance Preparation Prepare the line plot (pictured on page 9) for Part. For the optional Enrichment activity in Part, obtain a copy of the book Math Curse by Jon Scieszka and Lane Smith (Viking, 99). Teacher s Reference Manual, Grades pp Unit 8 Fractions

2 Getting Started Mental Math and Reflexes Pose problems like the following as children write the answers on slates. They may use tool-kit clocks as needed. minute = seconds 0 hour = minutes 0 _ hour = minutes 0 _ hour = minutes _ hour = minutes 0 _ hour = minutes _ hour = minutes 0 _ hour = minutes _ hour = minutes 0 Math Message Using your ruler, draw a line segment that is _ inches long on your slate. Divide the line segment into _ PROBL BLE -inch SO OLV segments. How many _ -inch segments are there? Home Link 8 7 Follow-Up Go over the answer to Problem. The diagram shows wholes and _ (or _ ) of a whole. The corresponding mixed number, then, is _ (or _ ). You may want to have children write number models for Problems. For example: Problem : _ + _ + _ + _ + _ + _ = _, or _, or _ Teaching the Lesson Math Message Follow-Up WHOLE-CLASS DISCUSSION If an overhead projector is available, use it to go over the solution. Lead children to the conclusion that since there are seven _ -inch segments, the line segment is 7_ inches long. 7_ inches is another name for _ inches. 0 Math Message solution Writing and Solving Fraction Number Stories WHOLE-CLASS You and the children make up stories involving fractions of sets. Children solve the problems in any way they can using pennies or counters, drawing pictures or doodles, and so on. You might want to begin with stories such as the following: Andy bought stamps for his stamp collection. _ of the stamps were from the United States. How many stamps were from the United States? 8 stamps Possible solution strategy: Take coins or counters and divide them into equal sets. Each set consists of counters and is _ of the total, so _ of =. Three sets consist of 8 counters and are _ of the total, so _ of = 8. 0 Adjusting the Activity Extend the line segment _ inch. Think of the line segment as part of a number line from 0 to. With children, label the points that are _ inch apart. AUDITORY KINESTHETIC TACTILE VISUAL Extending the line segment Ongoing Assessment: Informing Instruction Watch for children who are having difficulty solving problems with fractions of sets. Remind them that the denominator (the bottom number in a fraction) tells the total number of equal groups, and the numerator (the top number in a fraction) tells the number of equal groups being considered. Children count the objects in the number of groups given by the numerator to solve the problem. Have children use manipulatives to act out each problem. Lesson

3 Ruthann read books in the last months. Three were Adjusting the Activity Make up additional fraction number stories as appropriate before children solve problems independently. Use similar number stories in future Minute Math+ sessions. AUDITORY KINESTHETIC TACTILE VISUAL nonfiction. What fraction of the books were nonfiction? _ or _ of the books On average, how many books did she read per month? books Possible solution strategy: Three out of books is equivalent to _ of the total. Take counters and divide them into sets of. Each set is _ of the total. To find the average number read per month, divide by. Kiko has done _ of the math problems. What fraction of the math problems does she still have to do? _ of the problems Possible solution strategy: Suppose Kiko has problems to solve. She solved _ of the problems problems. This leaves problems still to be solved. Two out of problems is _ of the problems. Which would you rather have _ of a can of lemonade or _ of a can of lemonade? Assuming you like lemonade, _ of a can Possible solution strategy: Use Fraction Cards to compare the fractions, or reason as follows: _ is equivalent to _, which is less than _. Therefore, _ is more than _. Jim has $8. If he shares his money equally with 8 people, each person gets $8 8 = $ 8 = $; if he shares it equally with 8 people, each person gets $8 = $ 8 = $. If Jim doesn t share his money, how much money does he have? $8 Write a fraction to show how much money Jim has. $ 8 Possible solution strategy: The denominator names the number of people among whom Jim s $8 is divided. Since the money was not divided or shared with anyone but Jim, the denominator is. Since there are $8, 8 is the number in the numerator. $ 8 = $8 = $8 Which is the larger fraction, or? Possible solution strategy: The denominator tells how many parts the whole is divided into. For, the whole is divided into parts and is one of those parts. For, the whole is divided into part and there are wholes. = = So, is more than. It took Nathan _ hours to do his homework. How many minutes did he spend on homework? 7 minutes Possible solution strategy: hour = 0 minutes, _ hour = _ of 0 minutes, or minutes. Therefore, _ hours = 0 minutes + minutes = 7 minutes. 90 Unit 8 Fractions

4 Tamekka had 0 books to put into her bookcase. She put _ of the books on the top shelf and _ of the remaining books on the second shelf. How many books did she still need to put into the bookcase? books What fraction of the total number of books is that? _ of the total Possible solution strategy: _ of 0 = 0, so she put 0 books on the top shelf, which left 0 books to be shelved. She put _ of the remaining 0 books on the second shelf that s books. She put a total of 0 books + books, or books, into the bookcase which left books to be shelved. After working through a few examples, ask volunteers to make up stories for the class to solve. Solving Fraction Stories (Math Journal, pp. 00 and 0) Children work with a partner or independently to complete journal pages 00 and 0. PARTNER NOTE For practice with adding and subtracting fractions, go to Ongoing Assessment: Recognizing Student Achievement Journal page 0 Problems 0 Use journal page 0, Problems 0 to assess children s progress toward solving problems involving fractional parts of a collection. Children are making adequate progress if they are able to successfully complete Problems 0. Some children may successfully complete Problems. [Number and Numeration Goal ] Date Student Page Time Date Student Page Time LESSON 8 8 Fraction Number Stories Solve these number stories. Use pennies, counters, or draw pictures to help you.. There are 8 apples in the package. Glenn did not eat any. What fraction. Anik bought a dozen eggs at the supermarket. When he got home, he of the package did Glenn eat? found that of the eggs were cracked. How many eggs were cracked? 0 8 eggs LESSON 8 8 Fraction Number Stories continued 9. Write a fraction story. Ask your partner to solve it. Sample answer: Jerome gave new pens to his little sister. If the package had 0 pens in it, what fraction of the pens did he keep for himself? 8 0 of the pens. Chante used of a package of ribbon to wrap presents. Did she use more or less than of the package? less. There are 0 quarters. You have. I have. What fraction of the quarters do you have? 0 What fraction of the quarters do I have? 0 or What fraction of the quarters do we have together? 0 or. I had whole cookies. I gave you of cookie. How many cookies did I have left? cookies. One day, Edwin read of a book. The next day, he read another of the book. What fraction of the book had he read after days? What fraction of the book did he have left to read? Draw eggs in each carton to show the fraction. Sample answers: Example: Dorothy walks miles to school. Jaime walks miles to school. Who walks the longer distance? Neither; 8. Twelve children shared medium-size pizzas equally. What fraction of whole pizza did each child eat? or. Julie drank of a glass of juice. Draw an empty glass. Shade in the glass to show how much juice is left. Write the fraction. of the glass of juice is left. Math Journal, p. 00 Math Journal, p. 0 Lesson 8 8 9

5 Ongoing Learning & Practice Reviewing the Line Plot Routine (Student Reference Book, pp. 79 8) WHOLE-CLASS Use pages 79 8 in the Student Reference Book to review data landmarks. On the board, prepare a line plot with stick-on notes using this data:,,,,,,,,, 7, 7, 8, 8, 8, 8, 8, 0,,. To provide a context for children, suggest that the line plot shows the arm span measures in inches of a class of third graders. Number of Children Number of Inches Line plot of rd grade arm spans Ask children to identify the maximum arm span inches, the minimum arm span inches, the mode 8 inches, and the range inches from the line-plot data. Next, ask children to think of another way to find the median without removing the stick-on notes from the line plot. If no one suggests it, have volunteers cross out the first and last stick-on note from each end of the line plot over and over until one remains this is the median arm span. 7 inches Number of Children Number of Inches The median arm span is 7 inches. Have children imagine that you will put all the stick-on notes in a container and draw one out at random without looking. To practice comparing chances for two different events, pose the following: Compare the chance of drawing a note that says with the chance of getting a note that says 0. There is a greater chance of drawing than 0. Explain how you figured it out. There are two s and only one 0. 9 Unit 8 Fractions

6 Compare the chances of drawing and 7. The chances are equal because there are two s and two 7s. Compare the chances of drawing and 8. There is a greater chance of drawing 8 because there are five 8s and four s. Compare the chances of drawing 8 or a number larger than 8. There is a greater chance of drawing 8 because there are five 8s and only three numbers larger than 8. Math Boxes 8 8 (Math Journal, p. 0) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 8-. The skill in Problem previews Unit 9 content. Writing/Reasoning Have children draw or write an answer to the following: In Problem, is more or less than _? Use >, <, or = to compare the two fractions. > or < How do you know? Sample answer: is less than _ because of equal parts is less than of equal parts. Date LESSON 8 8 Math Boxes. Draw two ways to show. Sample answers:. Use simple drawings to show all of the possible ways you can take blocks from the bag.. Show two ways a team can score 7 points in a football game. Sample answer: 7 points points points points Write a number model: ( 7) ( ) ( ) 7; ( 7) ( ) 7 Student Page Time. feet yards feet 8 inches yards feet yards inches 7 Math Journal, p. 0. Tara frosted of the cupcakes. What fraction of the cupcakes is not frosted? Did she frost more or less than of the cupcakes? more If there were 0 cupcakes in all, how many did she frost? cupcakes. Use your calculator. Pretend the division key is broken. Solve this problem. Will, Wes, Sam, and Ameer want to share $ equally. How much money will each person get? Answer: $. Home Link 8 8 (Math Masters, p. ) INDEPENDENT Home Connection Children solve fraction number stories like those in the lesson. They solve multidigit addition and subtraction problems. Differentiation Options ENRICHMENT Solving Math Curse Number Stories SMALL-GROUP 0 Min To apply children s understanding of fraction concepts, read Math Curse and identify and solve the fraction problems in the story. Have children write their own fraction number stories based on daily activities, like those in Math Curse. The class can then discuss and solve these stories. Consider assembling the stories into a class book. Name Date Time HOME LINK 8 8 Family Note Home Link Master Fraction Number Stories In class we have been solving many kinds of fraction number stories. If some of these Home Link problems seem difficult, encourage your child to model them with pennies or draw pictures to help solve them. Please return this Home Link to school tomorrow. Solve these fraction stories. Use pennies, counters, or pictures to help.. Elizabeth bought a dozen eggs. She dropped her bag on the way home, and _ of the eggs broke. How many eggs broke? 8. Katie mowed _ of the lawn before lunch. What fraction of the lawn did she have to finish after lunch? eggs _ of the lawn. Donnie lives mile from school. One day he walked _ of the way to school when he remembered he had to return home to get a book. When he finally made it to school, how far did he walk in all? miles. Sheridan made trays of cookies. She took trays to school for her classmates. She took _ of a tray of cookies to her teacher. How many trays of cookies did Sheridan have left? _ trays. Jackson needed pints of milk for his recipe. If he had one gallon of milk in the refrigerator, how much did he use? _ (Hint: gallon = quarts, and quart = pints) gallon EXTRA PRACTICE Minute Math+ SMALL-GROUP Min To offer children more experience with fractions, see the following pages in Minute Math+: pp. 8, 90, 9, and. Practice Write these problems on the back of this page. Solve and show your work..,08 +,78 =,7 7.,7 -,80 =,908 8.,7 +,7 = 9, Math Masters, p. Unit Lesson 8 8 9